GIANO Data Reduction Software

The Giano Data Reduction Software (hereafter DrG) has been designed to run on different Unix/Linux platforms and relies on utilities available under the Unix public domain software. All data flow is through FITS and ASCII formats. The DrG back end has been entirely written in C99. We also plan to release a command-line version working in unattended automatic mode.

The DrG package will be provided with makefiles generated by Gnu automake and a configure script generated by Gnu autoconf. A small number of external libraries will be needed:

• glib-1.2.10 - required by gtk-1.2.10
• gtk-1.2.10 - the Gimp Tool Kit library
• gsl-1.5 - the Gnu Scientific Library
• cfitsio-2.5 - NASA's FITS File subroutine library
• fftw-3.0.1 - Fastest Fourier Transform in the West - only if needed

DrG back end

GIANO is an instrument with few observing modes, each of them producing quite a constant and repeatable distribution of light on the array. This allows to develop a highly optimized code: 2 main setups will be available for the high and low resolution, respectively. The DrG modules will be grouped in a few major tasks.

• Calibration Tools
  These tasks work on flat field and calibration lamp exposures and create tables with calibration coefficients. Given the stability of the instrument, the package will provide library calibration tables which can be used as standard calibration for scientific exposures. Calibration tools have been designed to work with a high degree of automation. Many tests have been carried out on a group of very inhomogeneous datasets from different instruments such as SARG@TNG, UVES@VLT, NIRSPEC@KECK, FEROS@ESO-MPI2.2m. By providing a configuration file with the instrumental parameters such as the camera focal length, detector pixel size, gain and read-out-noise, the echelle groove density, the nominal echelle blaze angle, a pipeline can be run to quickly produce calibrated spectra and some quality check in a fully automatic mode.
  • Order identification and geometry characterization: for each order it finds the polynomial which best fits the order center, the order width as a polynomial function of the x-coordinate and the range covered along the dispersion direction (x-axis). A check is also made to guarantee the completeness of the order detection. The task creates an output table with fitting coefficients.
  • Order line geometry: for each order it models the geometry variation of lines across the spectrum, first fitting the shape of each line from the calibration lamps with a polynomial, then looking for a global solution to model line shapes as a function of x-position and order number. Finally, for each order a reference grid is built and the geometric transformation to a linear space is saved in an output table.
  • Wavelength calibration: create an output table with computed coefficients for each order dispersion relation in a fully automatic fashion.

• Pre-reduction Tools
  The aim of these tasks is to transform a science exposure into a FITS file with straightened orders ready for the final extraction of monodimensional spectra. These tasks are carried out in a fully automatic mode.
  • Bad pixel and cosmic ray identification and flagging;
  • Sky Subtraction for two different setups: `telescope nodding on slit' and `telescope offsetting';
  • Flat Field correction: it optionally corrects for high frequency intensity variation across a flat field frame and normalizes the order mean values to 1;
  • Frame Resampling (order straightening): a flux-conserving resampling which maps the data to a geometric space where the echelle orders are parallel to an image axis and the wavelength dispersion is linear within each order.

• Reduction Tools
  • Object Aperture definition: it defines the y-range covered by the observed target inside each order;
  • 1-D spectrum extraction;
  • Optional correction for low frequency variations within the field of view;
  • Merging of spectra from different orders.

• Analysis Tools
  These tasks will work on extracted 1-D spectra and will provide some standard features such as continuum normalization, flux calibration, signal filtering, line profile analysis tools, spectra cross-correlation (to derive relative velocities between spectra), as well as a spectral line rest wavelength database, suitable to allow a fast access to spectral features of interest, especially for the on-line data quality assessment. The GUI will look like the popular DS9 display program: it will support multiple frame buffers, scaling and colormap manipulation, arbitrary zoom, pan and rotation, and obviously all the DrG Tools to give the user the opportunity to check interactively each step in the reduction and analysis process.

• Utilities Tools
  Some other utilities will be provided, such as a general purpose command line FITS calculator to allow the user to easily perform arithmetic computations of arbitrary complexity with any desired number of FITS images, also including computation of averages, weighted averages, median, etc.

Automatic Wavelength calibration

Wavelength calibration of echelle spectra usually requires the manual identification of a few lines from a calibration lamp exposure on at least three orders well distributed along the echellogram. By using a suitable atlas of spectral lines it is possible to compute a starting guess for the dispersion relation and iteratively refine it by adding more and more lines to the fitting process. Then a global dispersion formula can be fitted to combine the whole set of orders (in this way it is possible to get a more robust fit where only a few lines are visible, as in the red side of spectra).

At present the astronomical community seems to still lack a general software able to perform a wavelength calibration without predefined solutions or user interaction. This puts serious limits on the development of data reduction pipelines working in a completely unattended mode. With Giano DRS we have tried to overcome this lack, by developing a program that uses a starting guess for the order dispersion model which is accurate enough to achieve a good calibration without any user action. This is possible by making use of WCSLIB, a library developed by Mark Calabretta at the Australia Telescope National Facility to handle coordinate systems within FITS standards. According to the definitions in Greisen et al. 2006, we set:

$p$: Pixel coordinate (abscissa)

$q$: Intermediate pixel coordinate

$q1$: Corrected intermediate pixel coordinate

$x$: Intermediate world coordinate

$s$: World coordinate

where:

$q = p - {\rm CRPIX}_m$

$q1 = c_0 + c_1 \times q + c_2 \times q^2 + c_3 \times q^3 + \ldots$

$x = q1 \times {\rm CDELT}_m$

and CRPIX$_m$, CDELT$_m$ are the standard FITS keywords. Transformation from $x$ to $s$ (and back) is computed using spcx2s and spcs2x WCSLIB modules: these routines compute physical relations applicable for the dispersers commonly used in astronomical spectrographs to define a world coordinate function and derive spectral coordinates. The relation applies to the simple case of a single disperser and under the assumption that the radiation enters perpendicular to it. The requested physical parameters for such a transformation are the grating ruling density $\sigma$, the order number $m$, the angle of incidence $\beta$ and the CRVAL$_m$ ($\lambda$ value at reference point). For each order the following starting conditions are adopted:

$$q1 = q,$$ (1)

$${\rm CRVAL}_m = \frac{2.0 \times \sigma \times \sin (\beta) \times \cos (\gamma)}{m},$$ (2)

$${\rm CDELT}_m = \frac{\cos (\beta) \times \cos (\gamma)^2 \times \sigma \times {\rm pix\_size}}{f_{cam} \times m},$$ (3)

where $\rm pix\_size$ and $f_{cam}$ denote the detector pixel size and the camera focal length respectively. The 1st relation comes from the expected blaze wavelength, the 2nd from the expected linear dispersion at the central wavelength.

At a first stage, for each order the task looks for the CRPIX$_m$ value which maximizes the number of matches between observed and library lines. The linearity of the relations $m \times {\rm CRVAL}_m$ vs. $m$ and $m \times {\rm CDELT}_m$ vs. $m$ is used to distinguish each time well fitted orders from bad ones. In the second stage, the relation CRVAL$_m$ vs. $m$ is definitively fixed and the task proceeds to find order by order CRPIX$_m$ values and polynomial coefficents $c_0, c_1, \ldots, c_n$, progressively involving lines from the ends of the orders, where deviations from linearity are more severe, and increasing the degree of the polynomals. Much care has been used to avoid the incidence of false line matches as much as possible. Correctly modelled orders are used to derive a global dispersion relation which is suitable for all missing orders.

Some tests have been performed on data collected from different spectrographs, namely SARG, FEROS and NIRSPEC: the residuals of the wavelength calibrations showed a $\rm rms \approx 0.2 \div 0.23$ pixel, corresponding to $\rm rms \approx 0.009 \div 0.01$ Å.